All 3please urgent I need this answer in next 30min Q9 If α and β are the zeroes - Maths - Polynomials

Question

All 3please urgent I need this answer in next
30min

Q9 If α and β are the zeroes of the polynomial
x2 – 5x + 6, find a polynomial whose zeroes are
α   +   1 α - 1   and    
β   + 1 β   - 1

Amit Shukla · Accepted Answer

Dear Student,
We have,px = x2+x-2Since α and β are zeroes of px, thenα+β = -coefficient of xcoefficient of x2 = -1α×β = constant termcoefficient of x2 = -2Now in,1α-1β=β-ααβ=β-α-2 ----1now, we have,α+β=-1sqauring both sides w
r
t x, we get,α2+β2+2αβ=1α2+β2+2×-2=1α2+β2=5As we know,α-β2=α2+β2-2αββ-α2=5-2×-2=9β-α=±3Now, 1, we get;1α-1β=±3-2

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All 3please urgent I need this answer in next 30min Q9. If α and β are the zeroes of the polynomial x2 – 5x + 6, find a polynomial whose zeroes are α + 1 α - 1 and β + 1 β - 1 .

All 3please urgent I need this answer in next 30min

Q9. If $α$ and $β$ are the zeroes of the polynomial x² – 5x + 6, find a polynomial whose zeroes are $\frac{α + 1}{α - 1} and \frac{β + 1}{β - 1}$ .